How can I make a specific color on my model emit?
The weight factor of the red component is used for mix shader. The weight of the red component my be unsuitable. It may be too  small. If the red image has only red components keep this in mind for the math.  If red highlight image were actually bright white and black with maximum white values in some areas that would be desirable.  Multiply the weight of the red by 3 with a math node.  When red is normalized RGB->BW it may have been divided by three.  What you may have intended was ... to use the red color only as a basis for brightness and do not consider green and blue.  A single red color can only have 1/3 the brightness of bright white. Some mathematical liberties taken. It would be best if your red highlight image has very bright red areas.  Scaling by a value greater than 1, ... 3 or 4 for example,  will help to bring the brightness in the range you desire.  The highlight image may exist as black and white, rather than red, and be recolored to any other color in the Compositor.
Assuming you are using materials with emission shader. Increase the strength of emission for blinding brightness.
Your color curve may be unsuitable. All brightness may have been wiped out. Remedy. Make everything too bright.  Bring bright side to the middle.  Then reduce artistically.  My compositor color ramp may serve as an example.  Notice how the white color dominates most of the color ramp.
Know that the compositor can user Alpha Over node to lay images with transparency on top of one another.
Use an EMISSION shader and diffuse shader to the mix shader, if you continue to use the materials approach.  You clearly have a better chance of getting a bright color with the emission shader.
Compositor, compositing pixels, compositing nodes, with a color ramp can threshold colors and produce bright colors.  Next blur the edges.  Materials are a different approach.
Below is a compositor image of your original images.  I have used a color ramp to threshold the brightest color and dilated them to white.  White is easier to see then red. The border has not been removed.  This is an illustrative technique example not artistic for a single picture.   





Make sure you texture coordinates are correct for UV